Project 2: Theoretical analysis of functional modules (Fisher, years 1-3;Barkai, years 4-5) (#15-20) We have built and analyzed theoretical models and used them to predict and analyze the behavior of modules in vivo. We believe that mathematical models are needed to reach a full understanding of biological processes and two theorists have played major roles in the Center for Modular Biology. From 2002 to 2006, Daniel Fisher (Physics, now at Stanford) interacted with a number of groups on different problems, including the generation of segment polarity in Drosophila27, the factors that specify the length of the meiotic spindle (collaboration with T. Mitchison), and predicting the speed of evolution (collaboration with A. Murray). Experiments on the distribution and dynamics of microtubules suggest that microtubules are nucleated in a region near the chromosomes, and then transported polewards by a plus-end-directed motor (Eg5) that slides microtubules of opposite polarities past one another28. The model invokes competition between these motors and dynein, a minus-end-directed motor that clusters minus ends. Several predictions of this model have been confirmed by experiments29. We also produced a new theory for the rate of evolution in asexual populations and then performed experiments that confirmed key predictions of the theory and ruled out alternative models, including the extreme form of clonal interference. For the last two years, the PI on this project has been Naama Barkai;who has collaborated on projects examining the mating (project 3, collaboration with A. Murray) and sporulation (new project 6, collaboration with S. Ramanathan) of budding yeast. In mating, theory suggests that cells can decide between two equally attractive partners only if some of the protease that degrades mating pheromones is bound to the cell surface. We have refined this model and verified that successful discrimination requires cell-bound protease. Sporulation shows wide cell-to-cell variation. We have quantified the variable timing through the different steps of sporulation and are using theory and experiment to probe the molecular circuits that control sporulation, and ask how variability might be advantageous in a fluctuating environment. Finally, we have performed experiments to test the hypothesis that the presence of the TATA-box in promoter regions confers both noise and evolvability in gene expression (collaboration with A . Murray).